Question: Rewrite as a simplified fraction. ${0.7\overline{81} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 781.8181...\\ 10x &= 7.8181...\end{align*}}$ Subtracting the two equations, we have: ${990x = 774}$ ${x = \dfrac{774}{990}} $ ${x = \dfrac{43}{55}} $